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One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?

One Of The Five Quadratics Below Has A Repeated Root The Other Four Have Distinct Roots What Is The Repeated Root class=

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The quadratic equation with a repeated root is:

8*x^2 - 32*x  +32

And the repeated root is x = 2

What is the repeated root?

For a quadratic equation:

0 = a*x^2 + b*x + c

We define the discriminant as:

D = b^2 - 4ac

If D = 0, we have only one real root (or two repeated roots). Then we just need to see which of the given quadratic equations has a discriminant of zero.

1) -x^2 + 18x + 81

The discriminant is:

D = 18^2 - 4*(-1)*81 = 648

2) 3x^2 - 6x + 9

The discriminant is:

D = (-6)^2 - 4*3*9 = -72

3) 8*x^2 - 32*x  +32

The discriminant is:

D = (-32)^2 - 4*8*32 = 0

So this is the one with a discriminant of zero.

The roots are given by:

8*x^2 - 32*x  +32 = 0

Using Bhaskara's formula we will get:

x = (- (-32) ± √( (-32)^2 - 4*8*32))/(2*8)

x = (32/16) = 2

The repeated root is x = 2

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

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